AHC rating calculation

calc_perf.rb

S = 724.4744301
R = 0.8271973364

perfs = DATA.map(&:to_i)
Q = []

perfs.each do |perf|
  1.upto(100) do |j|
    Q << perf - S * Math.log(j)
  end 
end

Q.sort_by! { |q| -q }

numerator = (1..100).map { |i| Q[i - 1] * R ** i }.sum
denominator = (1..100).map { |i| R ** i }.sum

r = Rational(numerator, denominator)

if r < 400
  r = Rational(400, Math.exp(Rational(400 - r, 400)))
end

pp perfs
puts r.to_f

__END__
1861
1193
2464
1745
1889
2760
2699
2034
2978
1791
2199
3101
2287
2428
1605
2543
2102
2314
2485
3019
2701
1243
2355
2803

ref. https://www.dropbox.com/s/ne358pdixfafppm/AHC_rating.pdf?dl=0